{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

lecture note 4 - C2M2 Rational Fractions or Partial...

Info icon This preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
C2M2 Rational Fractions or Partial Fraction Decompositions When you were learning basic algebra there were probably problems assigned on adding fractions which had constants, linear expressions, and quadratic expressions in x in the numerators and denominators. Our objective here is to take the answers to those questions and find the fractions that were added together. The need here is to break down a complicated fraction into several simple ones whose anti-derivatives are (much!) easier to find. To approach this systematically we separate the problems into groups determined by the nature of the denominators of the fractions. Recall that P ( x ) = x 2 a 2 can be factored into P ( x ) = ( x a )( x + a ), so we say that P ( x ) is reducible . Likewise, Q ( x ) = x 2 + a 2 can NOT be factored, so Q ( x ) is irreducible . There are different approaches to to these problems and we will use substitution as our method. Two principles from algebra are applicable here. The first states that if two polynomials in x agree for all values of x , then the polynomials have the same coefficients, that is, they are identical. The second states that x r is a factor of the polynomial P ( x ) if and only if P ( r ) = 0.
Image of page 1

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern